ABSTRACTInsomnia is a common disorder linked with adverse long-term medical and psychiatric outcomes, but underlying pathophysiological processes and causal relationships with disease are poorly understood. Here we identify 57 loci for self-reported insomnia symptoms in the UK Biobank (n=453,379) and confirm their impact on self-reported insomnia symptoms in the HUNT study (n=14,923 cases, 47,610 controls), physician diagnosed insomnia in Partners Biobank (n=2,217 cases, 14,240 controls), and accelerometer-derived measures of sleep efficiency and sleep duration in the UK Biobank (n=83,726). Our results suggest enrichment of genes involved in ubiquitin-mediated proteolysis, phototransduction and muscle development pathways and of genes expressed in multiple brain regions, skeletal muscle and adrenal gland. Evidence of shared genetic factors is found between frequent insomnia symptoms and restless legs syndrome, aging, cardio-metabolic, behavioral, psychiatric and reproductive traits. Evidence is found for a possible causal link between insomnia symptoms and coronary heart disease, depressive symptoms and subjective well-being.One Sentence SummaryWe identify 57 genomic regions associated with insomnia pointing to the involvement of phototransduction and ubiquitination and potential causal links to CAD and depression.

AbstractUsing genome-wide data from 697,828 research participants from 23andMe and UK Biobank, we increase the number of identified loci associated with being a morning person, a behavioural indicator of a person’s underlying circadian rhythm, from 24 to 351. Using data from 85,760 individuals with activity-monitor derived measures of sleep timing we show that the chronotype loci influence sleep timing: the mean sleep timing of the 5% of individuals carrying the most “morningness” alleles was 25 minutes earlier than the 5% carrying the fewest. The loci were enriched for genes involved in circadian regulation, cAMP, glutamate and insulin signalling pathways, and those expressed in the retina, hindbrain, hypothalamus, and pituitary. We provide evidence that being a morning person is causally associated with better mental health but does not appear to affect BMI or Type 2 diabetes. This study offers new insights into the biology of circadian rhythms and links to disease in humans.

Inference for causal effects can benefit from the availability of an
instrumental variable (IV) which, by definition, is associated with the given
exposure, but not with the outcome of interest other than through a causal
exposure effect. Estimation methods for instrumental variables are now well
established for continuous outcomes, but much less so for dichotomous outcomes.
In this article we review IV estimation of so-called conditional causal odds
ratios which express the effect of an arbitrary exposure on a dichotomous
outcome conditional on the exposure level, instrumental variable and measured
covariates. In addition, we propose IV estimators of so-called marginal causal
odds ratios which express the effect of an arbitrary exposure on a dichotomous
outcome at the population level, and are therefore of greater public health
relevance. We explore interconnections between the different estimators and
support the results with extensive simulation studies and three applications.

AbstractMeta-analyses based on systematic literature reviews are commonly used to obtain a quantitative summary of the available evidence on a given topic. Despite its attractive simplicity, and its established position at the summit of the evidence-based medicine hierarchy, the reliability of any meta-analysis is largely constrained by the quality of its constituent studies. One major limitation is small study effects, whose presence can often easily be detected, but not so easily adjusted for. Here, robust methods of estimation based on the median and mode are proposed as tools to increase the reliability of findings in a meta-analysis. By re-examining data from published meta-analyses, and by conducting a detailed simulation study, we show that these two simple methods offer notable robustness to a range of plausible bias mechanisms, without making any explicit modelling assumptions. In conclusion, when performing a meta-analysis with suspected small study effects, we recommend reporting the mean, median and modal pooled estimates as a simple but informative sensitivity analyses.

Instrumental variable analysis is a widely used method to estimate causal
effects in the presence of unmeasured confounding. When the instruments,
exposure and outcome are not measured in the same sample, Angrist and Krueger
(1992) suggested to use two-sample instrumental variable (TSIV) estimators that
use sample moments from an instrument-exposure sample and an instrument-outcome
sample. However, this method is biased if the two samples are from
heterogeneous populations so that the distributions of the instruments are
different. In linear structural equation models, we derive a new class of TSIV
estimators that are robust to heterogeneous samples under the key assumption
that the structural relations in the two samples are the same. The widely used
two-sample two-stage least squares estimator belongs to this class. It is
generally not asymptotically efficient, although we find that it performs
similarly to the optimal TSIV estimator in most practical situations. We then
attempt to relax the linearity assumption. We find that, unlike one-sample
analyses, the TSIV estimator is not robust to misspecified exposure model.
Additionally, to nonparametrically identify the magnitude of the causal effect,
the noise in the exposure must have the same distributions in the two samples.
However, this assumption is in general untestable because the exposure is not
observed in one sample. Nonetheless, we may still identify the sign of the
causal effect in the absence of homogeneity of the noise.

ObjectiveAntitumour necrosis factor (anti-TNF) drugs impair protective immunity following pneumococcal, influenza and viral hepatitis vaccination and increase the risk of serious respiratory infections. We sought to determine whether infliximab-treated patients with IBD have attenuated serological responses to SARS-CoV-2 infections.DesignAntibody responses in participants treated with infliximab were compared with a reference cohort treated with vedolizumab, a gut-selective anti-integrin α4β7 monoclonal antibody that is not associated with impaired vaccine responses or increased susceptibility to systemic infections. 6935 patients were recruited from 92 UK hospitals between 22 September and 23 December 2020.ResultsRates of symptomatic and proven SARS-CoV-2 infection were similar between groups. Seroprevalence was lower in infliximab-treated than vedolizumab-treated patients (3.4% (161/4685) vs 6.0% (134/2250), p<0.0001). Multivariable logistic regression analyses confirmed that infliximab (vs vedolizumab; OR 0.66 (95% CI 0.51 to 0.87), p=0.0027) and immunomodulator use (OR 0.70 (95% CI 0.53 to 0.92), p=0.012) were independently associated with lower seropositivity. In patients with confirmed SARS-CoV-2 infection, seroconversion was observed in fewer infliximab-treated than vedolizumab-treated patients (48% (39/81) vs 83% (30/36), p=0.00044) and the magnitude of anti-SARS-CoV-2 reactivity was lower (median 0.8 cut-off index (0.2–5.6) vs 37.0 (15.2–76.1), p<0.0001).ConclusionsInfliximab is associated with attenuated serological responses to SARS-CoV-2 that were further blunted by immunomodulators used as concomitant therapy. Impaired serological responses to SARS-CoV-2 infection might have important implications for global public health policy and individual anti-TNF-treated patients. Serological testing and virus surveillance should be considered to detect suboptimal vaccine responses, persistent infection and viral evolution to inform public health policy.Trial registration numberISRCTN45176516.

A key assumption in Mendelian randomisation is that the relationship between the genetic instruments and the outcome is fully mediated by the exposure, known as the exclusion restriction assumption. However, in epidemiological studies, the exposure is often a coarsened approximation to some latent continuous trait. For example, latent liability to schizophrenia can be thought of as underlying the binary diagnosis measure. Genetically driven variation in the outcome can exist within categories of the exposure measurement, thus violating this assumption. We propose a framework to clarify this violation, deriving a simple expression for the resulting bias and showing that it may inflate or deflate effect estimates but will not reverse their sign. We then characterise a set of assumptions and a straight-forward method for estimating the effect of SD increases in the latent exposure. Our method relies on a sensitivity parameter which can be interpreted as the genetic variance of the latent exposure. We show that this method can be applied in both the one-sample and two-sample settings. We conclude by demonstrating our method in an applied example and reanalysing two papers which are likely to suffer from this type of bias, allowing meaningful interpretation of their effect sizes.

MR-PHeWAS is a powerful new design for discovering causal mechanisms between a disease and its many candidate risk factors in a hypothesis-free manner. This technique has great potential in the field of cancer research, provided that both powerful and principled statistical approaches are used.

Studies combined in a meta-analysis often have differences in their design and conduct that can lead to heterogeneous results. A random-effects model accounts for these differences in the underlying study effects, which includes a heterogeneity variance parameter. The DerSimonian-Laird method is often used to estimate the heterogeneity variance, but simulation studies have found the method can be biased and other methods are available. This paper compares the properties of nine different heterogeneity variance estimators using simulated meta-analysis data. Simulated scenarios include studies of equal size and of moderate and large differences in size. Results confirm that the DerSimonian-Laird estimator is negatively biased in scenarios with small studies and in scenarios with a rare binary outcome. Results also show the Paule-Mandel method has considerable positive bias in meta-analyses with large differences in study size. We recommend the method of restricted maximum likelihood (REML) to estimate the heterogeneity variance over other methods. However, considering that meta-analyses of health studies typically contain few studies, the heterogeneity variance estimate should not be used as a reliable gauge for the extent of heterogeneity in a meta-analysis. The estimated summary effect of the meta-analysis and its confidence interval derived from the Hartung-Knapp-Sidik-Jonkman method are more robust to changes in the heterogeneity variance estimate and show minimal deviation from the nominal coverage of 95% under most of our simulated scenarios.

BACKGROUND: Mendelian randomization (MR) is a powerful tool in epidemiology that can be used to estimate the causal effect of an exposure on an outcome in the presence of unobserved confounding, by utilizing genetic variants that are instrumental variables (IVs) for the exposure. This has been extended to multivariable MR (MVMR) to estimate the effect of two or more exposures on an outcome. METHODS AND RESULTS: We use simulations and theory to clarify the interpretation of estimated effects in a MVMR analysis under a range of underlying scenarios, where a secondary exposure acts variously as a confounder, a mediator, a pleiotropic pathway and a collider. We then describe how instrument strength and validity can be assessed for an MVMR analysis in the single-sample setting, and develop tests to assess these assumptions in the popular two-sample summary data setting. We illustrate our methods using data from UK Biobank to estimate the effect of education and cognitive ability on body mass index. CONCLUSION: MVMR analysis consistently estimates the direct causal effect of an exposure, or exposures, of interest and provides a powerful tool for determining causal effects in a wide range of scenarios with either individual- or summary-level data.

Insomnia is a common disorder linked with adverse long-term medical and psychiatric outcomes. The underlying pathophysiological processes and causal relationships of insomnia with disease are poorly understood. Here we identify 57 loci for self-reported insomnia symptoms in the UK Biobank (n = 453,379) and confirm their impact on self-reported insomnia symptoms in the HUNT study (n = 14,923 cases, 47,610 controls), physician-diagnosed insomnia in Partners Biobank (n = 2,217 cases, 14,240 controls), and accelerometer-derived measures of sleep efficiency and sleep duration in the UK Biobank (n = 83,726). Our results suggest enrichment of genes involved in ubiquitin-mediated proteolysis and of genes expressed in multiple brain regions, skeletal muscle, and adrenal gland. Evidence of shared genetic factors is found between frequent insomnia symptoms and restless legs syndrome, aging, cardio-metabolic, behavioral, psychiatric and reproductive traits. Evidence is found for a possible causal link between insomnia symptoms and coronary artery disease, depressive symptoms and subjective well-being.

BACKGROUND: Mendelian randomization (MR) has developed into an established method for strengthening causal inference and estimating causal effects, largely due to the proliferation of genome-wide association studies. However, genetic instruments remain controversial, as horizontal pleiotropic effects can introduce bias into causal estimates. Recent work has highlighted the potential of gene-environment interactions in detecting and correcting for pleiotropic bias in MR analyses. METHODS: We introduce MR using Gene-by-Environment interactions (MRGxE) as a framework capable of identifying and correcting for pleiotropic bias. If an instrument-covariate interaction induces variation in the association between a genetic instrument and exposure, it is possible to identify and correct for pleiotropic effects. The interpretation of MRGxE is similar to conventional summary MR approaches, with a particular advantage of MRGxE being the ability to assess the validity of an individual instrument. RESULTS: We investigate the effect of adiposity, measured using body mass index (BMI), upon systolic blood pressure (SBP) using data from the UK Biobank and a single weighted allelic score informed by data from the GIANT consortium. We find MRGxE produces findings in agreement with two-sample summary MR approaches. Further, we perform simulations highlighting the utility of the approach even when the MRGxE assumptions are violated. CONCLUSIONS: By utilizing instrument-covariate interactions in MR analyses implemented within a linear-regression framework, it is possible to identify and correct for horizontal pleiotropic bias, provided the average magnitude of pleiotropy is constant across interaction-covariate subgroups.

Using genome-wide data from 697,828 UK Biobank and 23andMe participants, we increase the number of identified loci associated with being a morning person, a behavioural indicator of a person’s underlying circadian rhythm, from 24 to 351. Using data from 85,760 individuals with activity-monitor derived measures of sleep timing we demonstrate that the chronotype loci influence sleep timing: the mean sleep timing of the 5% of individuals carrying the most morningness alleles is 25 minutes earlier than the 5% carrying the fewest. The loci are enriched for genes involved in circadian regulation, cAMP, glutamate and insulin signalling pathways, and those expressed in the retina, hindbrain, hypothalamus, and pituitary. Using Mendelian Randomisation, we show that being a morning person is causally associated with better mental health but does not affect BMI or risk of Type 2 diabetes. This study offers insights into circadian biology and its links to disease in humans.

Excessive daytime sleepiness (EDS) affects 10–20% of the population and is associated with substantial functional deficits. Here, we identify 42 loci for self-reported daytime sleepiness in GWAS of 452,071 individuals from the UK Biobank, with enrichment for genes expressed in brain tissues and in neuronal transmission pathways. We confirm the aggregate effect of a genetic risk score of 42 SNPs on daytime sleepiness in independent Scandinavian cohorts and on other sleep disorders (restless legs syndrome, insomnia) and sleep traits (duration, chronotype, accelerometer-derived sleep efficiency and daytime naps or inactivity). However, individual daytime sleepiness signals vary in their associations with objective short vs long sleep, and with markers of sleep continuity. The 42 sleepiness variants primarily cluster into two predominant composite biological subtypes - sleep propensity and sleep fragmentation. Shared genetic links are also seen with obesity, coronary heart disease, psychiatric diseases, cognitive traits and reproductive ageing.

Sleep is an essential state of decreased activity and alertness but molecular factors regulating sleep duration remain unknown. Through genome-wide association analysis in 446,118 adults of European ancestry from the UK Biobank, we identify 78 loci for self-reported habitual sleep duration (p 

BACKGROUND: Two-sample summary-data Mendelian randomization (MR) incorporating multiple genetic variants within a meta-analysis framework is a popular technique for assessing causality in epidemiology. If all genetic variants satisfy the instrumental variable (IV) and necessary modelling assumptions, then their individual ratio estimates of causal effect should be homogeneous. Observed heterogeneity signals that one or more of these assumptions could have been violated. METHODS: Causal estimation and heterogeneity assessment in MR require an approximation for the variance, or equivalently the inverse-variance weight, of each ratio estimate. We show that the most popular 'first-order' weights can lead to an inflation in the chances of detecting heterogeneity when in fact it is not present. Conversely, ostensibly more accurate 'second-order' weights can dramatically increase the chances of failing to detect heterogeneity when it is truly present. We derive modified weights to mitigate both of these adverse effects. RESULTS: Using Monte Carlo simulations, we show that the modified weights outperform first- and second-order weights in terms of heterogeneity quantification. Modified weights are also shown to remove the phenomenon of regression dilution bias in MR estimates obtained from weak instruments, unlike those obtained using first- and second-order weights. However, with small numbers of weak instruments, this comes at the cost of a reduction in estimate precision and power to detect a causal effect compared with first-order weighting. Moreover, first-order weights always furnish unbiased estimates and preserve the type I error rate under the causal null. We illustrate the utility of the new method using data from a recent two-sample summary-data MR analysis to assess the causal role of systolic blood pressure on coronary heart disease risk. CONCLUSIONS: We propose the use of modified weights within two-sample summary-data MR studies for accurately quantifying heterogeneity and detecting outliers in the presence of weak instruments. Modified weights also have an important role to play in terms of causal estimation (in tandem with first-order weights) but further research is required to understand their strengths and weaknesses in specific settings.

Recent analyses have shown educational attainment to be associated with a number of health outcomes. This association may, in part, be due to an effect of educational attainment on smoking behaviour. In this study, we apply a multivariable Mendelian randomisation design to determine whether the effect of educational attainment on smoking behaviour is due to educational attainment or general cognitive ability. We use individual data from the UK Biobank study (N = 120,050) and summary data from large GWA studies of educational attainment, cognitive ability and smoking behaviour. Our results show that more years of education are associated with a reduced likelihood of smoking that is not due to an effect of general cognitive ability on smoking behaviour. Given the considerable physical harms associated with smoking, the effect of educational attainment on smoking is likely to contribute to the health inequalities associated with differences in educational attainment.

BACKGROUND: Fibrinogen is an essential hemostatic factor and cardiovascular disease risk factor. Early attempts at evaluating the causal effect of fibrinogen on coronary heart disease (CHD) and myocardial infraction (MI) using Mendelian randomization (MR) used single variant approaches, and did not take advantage of recent genome-wide association studies (GWAS) or multi-variant, pleiotropy robust MR methodologies. METHODS AND FINDINGS: We evaluated evidence for a causal effect of fibrinogen on both CHD and MI using MR. We used both an allele score approach and pleiotropy robust MR models. The allele score was composed of 38 fibrinogen-associated variants from recent GWAS. Initial analyses using the allele score used a meta-analysis of 11 European-ancestry prospective cohorts, free of CHD and MI at baseline, to examine incidence CHD and MI. We also applied 2 sample MR methods with data from a prevalent CHD and MI GWAS. Results are given in terms of the hazard ratio (HR) or odds ratio (OR), depending on the study design, and associated 95% confidence interval (CI). In single variant analyses no causal effect of fibrinogen on CHD or MI was observed. In multi-variant analyses using incidence CHD cases and the allele score approach, the estimated causal effect (HR) of a 1 g/L higher fibrinogen concentration was 1.62 (CI = 1.12, 2.36) when using incident cases and the allele score approach. In 2 sample MR analyses that accounted for pleiotropy, the causal estimate (OR) was reduced to 1.18 (CI = 0.98, 1.42) and 1.09 (CI = 0.89, 1.33) in the 2 most precise (smallest CI) models, out of 4 models evaluated. In the 2 sample MR analyses for MI, there was only very weak evidence of a causal effect in only 1 out of 4 models. CONCLUSIONS: a small causal effect of fibrinogen on CHD is observed using multi-variant MR approaches which account for pleiotropy, but not single variant MR approaches. Taken together, results indicate that even with large sample sizes and multi-variant approaches MR analyses still cannot exclude the null when estimating the causal effect of fibrinogen on CHD, but that any potential causal effect is likely to be much smaller than observed in epidemiological studies.

Mendelian randomization (MR) uses genetic variants as instrumental variables to infer whether a risk factor causally affects a health outcome. Meta-analysis has been used historically in MR to combine results from separate epidemiological studies, with each study using a small but select group of genetic variants. In recent years, it has been used to combine genome-wide association study (GWAS) summary data for large numbers of genetic variants. Heterogeneity among the causal estimates obtained from multiple genetic variants points to a possible violation of the necessary instrumental variable assumptions. In this article, we provide a basic introduction to MR and the instrumental variable theory that it relies upon. We then describe how random effects models, meta-regression, and robust regression are being used to test and adjust for heterogeneity in order to improve the rigor of the MR approach.

OBJECTIVES: Sugar-sweetened beverage (SSB) consumption in Australian Aboriginal and Torres Strait Islander people is reported to be disproportionally high compared with the general Australian population. This review aimed to scope the literature documenting SSB consumption and interventions to reduce SSB consumption among Australian Aboriginal and Torres Strait Islander people. Findings will inform strategies to address SSB consumption in Aboriginal and Torres Strait Islander communities. METHODS: PubMed, SCOPUS, CINAHL, Informit, Joanna Briggs Institute EBP, Mura databases and grey literature were searched for articles published between January 1980 and June 2018. Studies were included if providing data specific to an Australian Aboriginal and/or Torres Strait Islander population's SSB consumption or an intervention that focused on reducing SSB consumption in this population. DESIGN: Systematic scoping review. RESULTS: 59 articles were included (1846 screened). While reported SSB consumption was high, there were age-related and community-related differences observed in some studies. Most studies were conducted in remote or rural settings. Implementation of nutrition interventions that included an SSB component has built progressively in remote communities since the 1980s with a growing focus on community-driven, culturally sensitive approaches. More recent studies have focused exclusively on SSB consumption. Key SSB-related intervention elements included incentivising healthier options; reducing availability of less-healthy options; nutrition education; multifaceted or policy implementation (store nutrition or government policy). CONCLUSIONS: There was a relatively large number of studies reporting data on SSB consumption and/or sales, predominantly from remote and rural settings. During analysis it was subjectively clear that the more impactful studies were those which were community driven or involved extensive community consultation and collaboration. Extracting additional SSB-specific consumption data from an existing nationally representative survey of Aboriginal and Torres Strait Islander people could provide detailed information for demographic subgroups and benchmarks for future interventions. It is recommended that a consistent, culturally appropriate, set of consumption measures be developed.

OBJECTIVE: the obesity paradox in which overweight/obesity is associated with mortality benefits is believed to be explained by confounding and reverse causality rather than by a genuine clinical benefit of excess body weight. We aimed to gain deeper insights into the paradox through analyzing mortality relationships with several adiposity measures; assessing subgroups with type 2 diabetes, with coronary heart disease (CHD), with cancer, and by smoking status; and adjusting for several confounders. RESEARCH DESIGN AND METHODS: We studied the general UK Biobank population (N = 502,631) along with three subgroups of people with type 2 diabetes (n = 23,842), CHD (n = 24,268), and cancer (n = 45,790) at baseline. A range of adiposity exposures were considered, including BMI (continuous and categorical), waist circumference, body fat percentage, and waist-to-hip ratio, and the outcome was all-cause mortality. We used Cox regression models adjusted for age, smoking status, deprivation index, education, and disease history. RESULTS: for BMI, the obesity paradox was observed among people with type 2 diabetes (adjusted hazard ratio for obese vs. normal BMI 0.78 [95% CI 0.65, 0.95]) but not among those with CHD (1.00 [0.86, 1.17]). The obesity paradox was pronounced in current smokers, absent in never smokers, and more pronounced in men than in women. For other adiposity measures, there was less evidence for an obesity paradox, yet smoking status consistently modified the adiposity-mortality relationship. CONCLUSIONS: the obesity paradox was observed in people with type 2 diabetes and is heavily modified by smoking status. The results of subgroup analyses and statistical adjustments are consistent with reverse causality and confounding.

BACKGROUND: Pubertal timing has psychological and physical sequelae. While observational studies have demonstrated an association between age at menarche and adult body mass index (BMI), confounding makes it difficult to infer causality. METHODS: the Mendelian randomization (MR) technique is not limited by traditional confounding and was used to investigate the presence of a causal effect of age at menarche on adult BMI. MR uses genetic variants as instruments under the assumption that they act on BMI only through age at menarche (no pleiotropy). Using a two-sample MR approach, heterogeneity between the MR estimates from individual instruments was used as a proxy for pleiotropy, with sensitivity analyses performed if detected. Genetic instruments and estimates of their association with age at menarche were obtained from a genome-wide association meta-analysis on 182,416 women. The genetic effects on adult BMI were estimated using data on 80,465 women from the UK Biobank. The presence of a causal effect of age at menarche on adult BMI was further investigated using data on 70,692 women from the GIANT Consortium. RESULTS: There was evidence of pleiotropy among instruments. Using the UK Biobank data, after removing instruments associated with childhood BMI that were likely exerting pleiotropy, fixed-effect meta-analysis across instruments demonstrated that a 1 year increase in age at menarche reduces adult BMI by 0.38 kg/m2 (95% CI 0.25-0.51 kg/m2). However, evidence of pleiotropy remained. MR-Egger regression did not suggest directional bias, and similar estimates to the fixed-effect meta-analysis were obtained in sensitivity analyses when using a random-effect model, multivariable MR, MR-Egger regression, a weighted median estimator and a weighted mode-based estimator. The direction and significance of the causal effect were replicated using GIANT Consortium data. CONCLUSION: MR provides evidence to support the hypothesis that earlier age at menarche causes higher adult BMI. Complex hormonal and psychological factors may be responsible.

BACKGROUND: Observational studies on pubertal timing and asthma, mainly performed in females, have provided conflicting results about a possible association of early puberty with higher risk of adult asthma, possibly due to residual confounding. To overcome issues of confounding, we used Mendelian randomisation (MR), i.e. genetic variants were used as instrumental variables to estimate causal effects of early puberty on post-pubertal asthma in both females and males. METHODS AND FINDINGS: MR analyses were performed in UK Biobank on 243,316 women using 254 genetic variants for age at menarche, and on 192,067 men using 46 variants for age at voice breaking. Age at menarche, recorded in years, was categorised as early (14); age at voice breaking was recorded and analysed as early (younger than average), normal (about average age), or late (older than average). In females, we found evidence for a causal effect of pubertal timing on asthma, with an 8% increase in asthma risk for early menarche (odds ratio [OR] 1.08; 95% CI 1.04 to 1.12; p = 8.7 × 10(-5)) and an 8% decrease for late menarche (OR 0.92; 95% CI 0.89 to 0.97; p = 3.4 × 10(-4)), suggesting a continuous protective effect of increasing age at puberty. In males, we found very similar estimates of causal effects, although with wider confidence intervals (early voice breaking: OR 1.07; 95% CI 1.00 to 1.16; p = 0.06; late voice breaking: OR 0.93; 95% CI 0.87 to 0.99; p = 0.03). We detected only modest pleiotropy, and our findings showed robustness when different methods to account for pleiotropy were applied. BMI may either introduce pleiotropy or lie on the causal pathway; secondary analyses excluding variants associated with BMI yielded similar results to those of the main analyses. Our study relies on self-reported exposures and outcomes, which may have particularly affected the power of the analyses on age at voice breaking. CONCLUSIONS: This large MR study provides evidence for a causal detrimental effect of early puberty on asthma, and does not support previous observational findings of a U-shaped relationship between pubertal timing and asthma. Common biological or psychological mechanisms associated with early puberty might explain the similarity of our results in females and males, but further research is needed to investigate this. Taken together with evidence for other detrimental effects of early puberty on health, our study emphasises the need to further investigate and address the causes of the secular shift towards earlier puberty observed worldwide.

Objectives to identify the genetic determinants of fracture risk and assess the role of 15 clinical risk factors on osteoporotic fracture risk. Design Meta-analysis of genome wide association studies (GWAS) and a two-sample mendelian randomisation approach. Setting 25 cohorts from Europe, United States, east Asia, and Australia with genome wide genotyping and fracture data. Participants a discovery set of 37 857 fracture cases and 227 116 controls; with replication in up to 147 200 fracture cases and 150 085 controls. Fracture cases were defined as individuals (>18 years old) who had fractures at any skeletal site confirmed by medical, radiological, or questionnaire reports. Instrumental variable analyses were performed to estimate effects of 15 selected clinical risk factors for fracture in a two-sample mendelian randomisation framework, using the largest previously published GWAS meta-analysis of each risk factor. Results of 15 fracture associated loci identified, all were also associated with bone mineral density and mapped to genes clustering in pathways known to be critical to bone biology (eg, SOST, WNT16, and ESR1) or novel pathways (FAM210A, GRB10, and ETS2). Mendelian randomisation analyses showed a clear effect of bone mineral density on fracture risk. One standard deviation decrease in genetically determined bone mineral density of the femoral neck was associated with a 55% increase in fracture risk (odds ratio 1.55 (95% confidence interval 1.48 to 1.63; P=1.5×10'68). Hand grip strength was inversely associated with fracture risk, but this result was not significant after multiple testing correction. The remaining clinical risk factors (including vitamin D levels) showed no evidence for an effect on fracture. Conclusions This large scale GWAS meta-analysis for fracture identified 15 genetic determinants of fracture, all of which also influenced bone mineral density. Among the clinical risk factors for fracture assessed, only bone mineral density showed a major causal effect on fracture. Genetic predisposition to lower levels of vitamin D and estimated calcium intake from dairy sources were not associated with fracture risk.

Pleiotropy, the phenomenon of a single genetic variant influencing multiple traits, is likely widespread in the human genome. If pleiotropy arises because the single nucleotide polymorphism (SNP) influences one trait, which in turn influences another ('vertical pleiotropy'), then Mendelian randomization (MR) can be used to estimate the causal influence between the traits. of prime focus among the many limitations to MR is the unprovable assumption that apparent pleiotropic associations are mediated by the exposure (i.e. reflect vertical pleiotropy), and do not arise due to SNPs influencing the two traits through independent pathways ('horizontal pleiotropy'). The burgeoning treasure trove of genetic associations yielded through genome wide association studies makes for a tantalizing prospect of phenome-wide causal inference. Recent years have seen substantial attention devoted to the problem of horizontal pleiotropy, and in this review we outline how newly developed methods can be used together to improve the reliability of MR.

Background: data furnishing a two-sample Mendelian randomization (MR) study are often visualized with the aid of a scatter plot, in which single-nucleotide polymorphism (SNP)-outcome associations are plotted against the SNP-exposure associations to provide an immediate picture of the causal-effect estimate for each individual variant. It is also convenient to overlay the standard inverse-variance weighted (IVW) estimate of causal effect as a fitted slope, to see whether an individual SNP provides evidence that supports, or conflicts with, the overall consensus. Unfortunately, the traditional scatter plot is not the most appropriate means to achieve this aim whenever SNP-outcome associations are estimated with varying degrees of precision and this is reflected in the analysis. Methods: We propose instead to use a small modification of the scatter plot-the Galbraith Radial plot-for the presentation of data and results from an MR study, which enjoys many advantages over the original method. On a practical level, it removes the need to recode the genetic data and enables a more straightforward detection of outliers and influential data points. Its use extends beyond the purely aesthetic, however, to suggest a more general modelling framework to operate within when conducting an MR study, including a new form of MR-Egger regression. Results: We illustrate the methods using data from a two-sample MR study to probe the causal effect of systolic blood pressure on coronary heart disease risk, allowing for the possible effects of pleiotropy. The Radial plot is shown to aid the detection of a single outlying variant that is responsible for large differences between IVW and MR-Egger regression estimates. Several additional plots are also proposed for informative data visualization. Conclusions: the Radial plot should be considered in place of the scatter plot for visualizing, analysing and interpreting data from a two-sample summary data MR study. Software is provided to help facilitate its use.

Background: Lower educational attainment is associated with increased rates of smoking, but ascertaining causality is challenging. We used two-sample Mendelian randomization (MR) analyses of summary statistics to examine whether educational attainment is causally related to smoking. Methods and Findings: We used summary statistics from genome-wide association studies (GWAS) of educational attainment and a range of smoking phenotypes (smoking initiation, cigarettes per day, cotinine levels and smoking cessation). of 74 single nucleotide polymorphisms (SNPs) that predict educational attainment, 57 (or their highly correlated proxies) were present in the smoking initiation, cigarettes per day and smoking cessation GWAS, and 72 in the cotinine GWAS. Various complementary MR techniques (inverse variance weighted regression, MR Egger, weighted median regression) were used to test the robustness of our results. We found broadly consistent evidence across these techniques that higher educational attainment leads to reduced likelihood of smoking initiation, reduced heaviness of smoking among smokers (as measured via self-report [e.g. inverse variance weighted beta -2.25, 95% confidence interval (CI) -3.81, -0.70, P = 0.005] and cotinine levels [e.g. inverse variance weighted beta -0.34, 95% CI -0.67, -0.01, P = 0.057]), and greater likelihood of smoking cessation among smokers (inverse variance weighted beta 0.65, 95% CI 0.35, 0.95, P = 5.54 × 10-5). Less consistent across the different techniques were associations between educational attainment and smoking initiation. Conclusions: Our findings indicate a causal association between low educational attainment and increased risk of smoking, and may explain the observational associations between educational attainment and adverse health outcomes such as risk of coronary heart disease.

Mendelian randomization (MR) is gaining in recognition and popularity as a method for strengthening causal inference in epidemiology by utilizing genetic variants as instrumental variables. Concurrently with the explosion in empirical MR studies, there has been the steady production of new approaches for MR analysis. The recently proposed "global and individual tests for direct effects" (GLIDE) approach fits into a family of methods that aim to detect horizontal pleiotropy-at the individual single nucleotide polymorphism level and at the global level-and to adjust the analysis by removing outlying single nucleotide polymorphisms. In this commentary, we explain how existing methods can (and indeed are) being used to detect pleiotropy at the individual and global levels, although not explicitly using this terminology. By doing so, we show that the true comparator for GLIDE is not MR-Egger regression (as Dai et al. the authors of the accompanying article (Am J Epidemiol. 2018;187(12):2672-2680), claim) but rather the humble heterogeneity statistic.

Response-adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients-referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2-armed and the multi-armed case. We further propose a RAR design for multi-armed clinical trials, which is computationally efficient and robust to several time trends considered.

Results from genome-wide association studies (GWAS) can be used to infer causal relationships between phenotypes, using a strategy known as 2-sample Mendelian randomization (2SMR) and bypassing the need for individual-level data. However, 2SMR methods are evolving rapidly and GWAS results are often insufficiently curated, undermining efficient implementation of the approach. We therefore developed MR-Base (http://www.mrbase.org): a platform that integrates a curated database of complete GWAS results (no restrictions according to statistical significance) with an application programming interface, web app and R packages that automate 2SMR. The software includes several sensitivity analyses for assessing the impact of horizontal pleiotropy and other violations of assumptions. The database currently comprises 11 billion single nucleotide polymorphism-trait associations from 1673 GWAS and is updated on a regular basis. Integrating data with software ensures more rigorous application of hypothesis-driven analyses and allows millions of potential causal relationships to be efficiently evaluated in phenome-wide association studies.

BACKGROUND: Network meta-analysis (NMA) allows for the estimation of comparative effectiveness of treatments that have not been studied in head-to-head trials; however, relative treatment effects for all interventions can only be derived where available evidence forms a connected network. Head-to-head evidence is limited in many disease areas, regularly resulting in disconnected evidence structures where a large number of treatments are available. This is also the case in the evidence of treatments for relapsed or refractory multiple myeloma. METHODS: Randomised controlled trials (RCTs) identified in a systematic literature review form two disconnected evidence networks. Standard Bayesian NMA models are fitted to obtain estimates of relative effects within each network. Observational evidence was identified to fill the evidence gap. Single armed trials are matched to act as each other's control group based on a distance metric derived from covariate information. Uncertainty resulting from including this evidence is incorporated by analysing the space of possible matches. RESULTS: Twenty five randomised controlled trials form two disconnected evidence networks; 12 single armed observational studies are considered for bridging between the networks. Five matches are selected to bridge between the networks. While significant variation in the ranking is observed, daratumumab in combination with dexamethasone and either lenalidomide or bortezomib, as well as triple therapy of carfilzomib, ixazomib and elozumatab, in combination with lenalidomide and dexamethasone, show the highest effects on progression free survival, on average. CONCLUSIONS: the analysis shows how observational data can be used to fill gaps in the existing networks of RCT evidence; allowing for the indirect comparison of a large number of treatments, which could not be compared otherwise. Additional uncertainty is accounted for by scenario analyses reducing the risk of over confidence in interpretation of results.

Mendelian randomization (MR) uses genetic data to probe questions of causality in epidemiological research, by invoking the Instrumental Variable (IV) assumptions. In recent years, it has become commonplace to attempt MR analyses by synthesising summary data estimates of genetic association gleaned from large and independent study populations. This is referred to as two-sample summary data MR. Unfortunately, due to the sheer number of variants that can be easily included into summary data MR analyses, it is increasingly likely that some do not meet the IV assumptions due to pleiotropy. There is a pressing need to develop methods that can both detect and correct for pleiotropy, in order to preserve the validity of the MR approach in this context. In this paper, we aim to clarify how established methods of meta-regression and random effects modelling from mainstream meta-analysis are being adapted to perform this task. Specifically, we focus on two contrastin g approaches: the Inverse Variance Weighted (IVW) method which assumes in its simplest form that all genetic variants are valid IVs, and the method of MR-Egger regression that allows all variants to violate the IV assumptions, albeit in a specific way. We investigate the ability of two popular random effects models to provide robustness to pleiotropy under the IVW approach, and propose statistics to quantify the relative goodness-of-fit of the IVW approach over MR-Egger regression. © 2017 the Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.

Multi-arm multi-stage trials can improve the efficiency of the drug development process when multiple new treatments are available for testing. A group-sequential approach can be used in order to design multi-arm multi-stage trials, using an extension to Dunnett's multiple-testing procedure. The actual sample size used in such a trial is a random variable that has high variability. This can cause problems when applying for funding as the cost will also be generally highly variable. This motivates a type of design that provides the efficiency advantages of a group-sequential multi-arm multi-stage design, but has a fixed sample size. One such design is the two-stage drop-the-losers design, in which a number of experimental treatments, and a control treatment, are assessed at a prescheduled interim analysis. The best-performing experimental treatment and the control treatment then continue to a second stage. In this paper, we discuss extending this design to have more than two stages, which is shown to considerably reduce the sample size required. We also compare the resulting sample size requirements to the sample size distribution of analogous group-sequential multi-arm multi-stage designs. The sample size required for a multi-stage drop-the-losers design is usually higher than, but close to, the median sample size of a group-sequential multi-arm multi-stage trial. In many practical scenarios, the disadvantage of a slight loss in average efficiency would be overcome by the huge advantage of a fixed sample size. We assess the impact of delay between recruitment and assessment as well as unknown variance on the drop-the-losers designs.

Longitudinal studies are often used to investigate age-related developmental change. Whereas a single cohort design takes a group of individuals at the same initial age and follows them over time, an accelerated longitudinal design takes multiple single cohorts, each one starting at a different age. The main advantage of an accelerated longitudinal design is its ability to span the age range of interest in a shorter period of time than would be possible with a single cohort longitudinal design. This paper considers design issues for accelerated longitudinal studies. A linear mixed effect model is considered to describe the responses over age with random effects for intercept and slope parameters. Random and fixed cohort effects are used to cope with the potential bias accelerated longitudinal designs have due to multiple cohorts. The impact of other factors such as costs and the impact of dropouts on the power of testing or the precision of estimating parameters are examined. As duration-related costs increase relative to recruitment costs the best designs shift towards shorter duration and eventually cross-sectional design being best. For designs with the same duration but differing interval between measurements, we found there was a cutoff point for measurement costs relative to recruitment costs relating to frequency of measurements. Under our model of 30% dropout there was a maximum power loss of 7%.

BACKGROUND: Observational associations between cannabis and schizophrenia are well documented, but ascertaining causation is more challenging. We used Mendelian randomization (MR), utilizing publicly available data as a method for ascertaining causation from observational data. METHOD: We performed bi-directional two-sample MR using summary-level genome-wide data from the International Cannabis Consortium (ICC) and the Psychiatric Genomics Consortium (PGC2). Single nucleotide polymorphisms (SNPs) associated with cannabis initiation (p < 10-5) and schizophrenia (p < 5 × 10-8) were combined using an inverse-variance-weighted fixed-effects approach. We also used height and education genome-wide association study data, representing negative and positive control analyses. RESULTS: There was some evidence consistent with a causal effect of cannabis initiation on risk of schizophrenia [odds ratio (OR) 1.04 per doubling odds of cannabis initiation, 95% confidence interval (CI) 1.01-1.07, p = 0.019]. There was strong evidence consistent with a causal effect of schizophrenia risk on likelihood of cannabis initiation (OR 1.10 per doubling of the odds of schizophrenia, 95% CI 1.05-1.14, p = 2.64 × 10-5). Findings were as predicted for the negative control (height: OR 1.00, 95% CI 0.99-1.01, p = 0.90) but weaker than predicted for the positive control (years in education: OR 0.99, 95% CI 0.97-1.00, p = 0.066) analyses. CONCLUSIONS: Our results provide some that cannabis initiation increases the risk of schizophrenia, although the size of the causal estimate is small. We find stronger evidence that schizophrenia risk predicts cannabis initiation, possibly as genetic instruments for schizophrenia are stronger than for cannabis initiation.

Importance: the causal direction and magnitude of the association between telomere length and incidence of cancer and non-neoplastic diseases is uncertain owing to the susceptibility of observational studies to confounding and reverse causation. Objective: to conduct a Mendelian randomization study, using germline genetic variants as instrumental variables, to appraise the causal relevance of telomere length for risk of cancer and non-neoplastic diseases. Data Sources: Genomewide association studies (GWAS) published up to January 15, 2015. Study Selection: GWAS of noncommunicable diseases that assayed germline genetic variation and did not select cohort or control participants on the basis of preexisting diseases. of 163 GWAS of noncommunicable diseases identified, summary data from 103 were available. Data Extraction and Synthesis: Summary association statistics for single nucleotide polymorphisms (SNPs) that are strongly associated with telomere length in the general population. Main Outcomes and Measures: Odds ratios (ORs) and 95% confidence intervals (CIs) for disease per standard deviation (SD) higher telomere length due to germline genetic variation. Results: Summary data were available for 35 cancers and 48 non-neoplastic diseases, corresponding to 420 081 cases (median cases, 2526 per disease) and 1 093 105 controls (median, 6789 per disease). Increased telomere length due to germline genetic variation was generally associated with increased risk for site-specific cancers. The strongest associations (ORs [95% CIs] per 1-SD change in genetically increased telomere length) were observed for glioma, 5.27 (3.15-8.81); serous low-malignant-potential ovarian cancer, 4.35 (2.39-7.94); lung adenocarcinoma, 3.19 (2.40-4.22); neuroblastoma, 2.98 (1.92-4.62); bladder cancer, 2.19 (1.32-3.66); melanoma, 1.87 (1.55-2.26); testicular cancer, 1.76 (1.02-3.04); kidney cancer, 1.55 (1.08-2.23); and endometrial cancer, 1.31 (1.07-1.61). Associations were stronger for rarer cancers and at tissue sites with lower rates of stem cell division. There was generally little evidence of association between genetically increased telomere length and risk of psychiatric, autoimmune, inflammatory, diabetic, and other non-neoplastic diseases, except for coronary heart disease (OR, 0.78 [95% CI, 0.67-0.90]), abdominal aortic aneurysm (OR, 0.63 [95% CI, 0.49-0.81]), celiac disease (OR, 0.42 [95% CI, 0.28-0.61]) and interstitial lung disease (OR, 0.09 [95% CI, 0.05-0.15]). Conclusions and Relevance: it is likely that longer telomeres increase risk for several cancers but reduce risk for some non-neoplastic diseases, including cardiovascular diseases.

BACKGROUND AND AIMS: Coffee consumption and cigarette smoking are strongly associated, but whether this association is causal remains unclear. We sought to: (1) determine whether coffee consumption influences cigarette smoking causally, (2) estimate the magnitude of any association and (3) explore potential mechanisms. DESIGN: We used Mendelian randomization (MR) analyses of observational data, using publicly available summarized data from the Tobacco and Genetics (TAG) consortium, individual-level data from the UK Biobank and in-vitro experiments of candidate compounds. SETTING: the TAG consortium includes data from studies in several countries. The UK Biobank includes data from men and women recruited across England, Wales and Scotland. PARTICIPANTS: the TAG consortium provided data on n ≤ 38 181 participants. The UK Biobank provided data on 8072 participants. MEASUREMENTS: in MR analyses, the exposure was coffee consumption (cups/day) and the outcome was heaviness of smoking (cigarettes/day). In our in-vitro experiments we assessed the effect of caffeic acid, quercetin and p-coumaric acid on the rate of nicotine metabolism in human liver microsomes and cDNA-expressed human CYP2A6. FINDINGS: Two-sample MR analyses of TAG consortium data indicated that heavier coffee consumption might lead to reduced heaviness of smoking [beta = -1.49, 95% confidence interval (CI) = -2.88 to -0.09]. However, in-vitro experiments found that the compounds investigated are unlikely to inhibit significantly the rate of nicotine metabolism following coffee consumption. Further MR analyses in UK Biobank found no evidence of a causal relationship between coffee consumption and heaviness of smoking (beta = 0.20, 95% CI = -1.72 to 2.12). CONCLUSIONS: Amount of coffee consumption is unlikely to have a major causal impact upon amount of cigarette smoking. If it does influence smoking, this is not likely to operate via effects of caffeic acid, quercetin or p-coumaric acid on nicotine metabolism. The observational association between coffee consumption and cigarette smoking may be due to smoking impacting on coffee consumption or confounding.

Objective To determine whether educational attainment is a causal risk factor in the development of coronary heart disease.Design Mendelian randomisation study, using genetic data as proxies for education to minimise confounding.Setting The main analysis used genetic data from two large consortia (CARDIoGRAMplusC4D and SSGAC), comprising 112 studies from predominantly high income countries. Findings from mendelian randomisation analyses were then compared against results from traditional observational studies (164 170 participants). Finally, genetic data from six additional consortia were analysed to investigate whether longer education can causally alter the common cardiovascular risk factors.Participants The main analysis was of 543 733 men and women (from CARDIoGRAMplusC4D and SSGAC), predominantly of European origin.Exposure A one standard deviation increase in the genetic predisposition towards higher education (3.6 years of additional schooling), measured by 162 genetic variants that have been previously associated with education.Main outcome measure Combined fatal and non-fatal coronary heart disease (63 746 events in CARDIoGRAMplusC4D).Results Genetic predisposition towards 3.6 years of additional education was associated with a one third lower risk of coronary heart disease (odds ratio 0.67, 95% confidence interval 0.59 to 0.77; P=3×10-8). This was comparable to findings from traditional observational studies (prevalence odds ratio 0.73, 0.68 to 0.78; incidence odds ratio 0.80, 0.76 to 0.83). Sensitivity analyses were consistent with a causal interpretation in which major bias from genetic pleiotropy was unlikely, although this remains an untestable possibility. Genetic predisposition towards longer education was additionally associated with less smoking, lower body mass index, and a favourable blood lipid profile.Conclusions This mendelian randomisation study found support for the hypothesis that low education is a causal risk factor in the development of coronary heart disease. Potential mechanisms could include smoking, body mass index, and blood lipids. In conjunction with the results from studies with other designs, these findings suggest that increasing education may result in substantial health benefits.

Chronic sleep disturbances, associated with cardiometabolic diseases, psychiatric disorders and all-cause mortality, affect 25-30% of adults worldwide. Although environmental factors contribute substantially to self-reported habitual sleep duration and disruption, these traits are heritable and identification of the genes involved should improve understanding of sleep, mechanisms linking sleep to disease and development of new therapies. We report single- and multiple-trait genome-wide association analyses of self-reported sleep duration, insomnia symptoms and excessive daytime sleepiness in the UK Biobank (n = 112,586). We discover loci associated with insomnia symptoms (near MEIS1, TMEM132E, CYCL1 and TGFBI in females and WDR27 in males), excessive daytime sleepiness (near AR-OPHN1) and a composite sleep trait (near PATJ (INADL) and HCRTR2) and replicate a locus associated with sleep duration (at PAX8). We also observe genetic correlation between longer sleep duration and schizophrenia risk (rg = 0.29, P = 1.90 × 10-13) and between increased levels of excessive daytime sleepiness and increased measures for adiposity traits (body mass index (BMI): rg = 0.20, P = 3.12 × 10-9; waist circumference: rg = 0.20, P = 2.12 × 10-7).

Importance: Positive associations between inflammatory biomarkers and risk of psychiatric disorders, including schizophrenia, have been reported in observational studies. However, conventional observational studies are prone to bias, such as reverse causation and residual confounding, thus limiting our understanding of the effect (if any) of inflammatory biomarkers on schizophrenia risk. Objective: to evaluate whether inflammatory biomarkers have an effect on the risk of developing schizophrenia. Design, Setting, and Participants: Two-sample mendelian randomization study using genetic variants associated with inflammatory biomarkers as instrumental variables to improve inference. Summary association results from large consortia of candidate gene or genome-wide association studies, including several epidemiologic studies with different designs, were used. Gene-inflammatory biomarker associations were estimated in pooled samples ranging from 1645 to more than 80 000 individuals, while gene-schizophrenia associations were estimated in more than 30 000 cases and more than 45 000 ancestry-matched controls. In most studies included in the consortia, participants were of European ancestry, and the prevalence of men was approximately 50%. All studies were conducted in adults, with a wide age range (18 to 80 years). Exposures: Genetically elevated circulating levels of C-reactive protein (CRP), interleukin-1 receptor antagonist (IL-1Ra), and soluble interleukin-6 receptor (sIL-6R). Main Outcomes and Measures: Risk of developing schizophrenia. Individuals with schizophrenia or schizoaffective disorders were included as cases. Given that many studies contributed to the analyses, different diagnostic procedures were used. Results: the pooled odds ratio estimate using 18 CRP genetic instruments was 0.90 (random effects 95% CI, 0.84-0.97; P = .005) per 2-fold increment in CRP levels; consistent results were obtained using different mendelian randomization methods and a more conservative set of instruments. The odds ratio for sIL-6R was 1.06 (95% CI, 1.01-1.12; P = .02) per 2-fold increment. Estimates for IL-1Ra were inconsistent among instruments, and pooled estimates were imprecise and centered on the null. Conclusions and Relevance: Under mendelian randomization assumptions, our findings suggest a protective effect of CRP and a risk-increasing effect of sIL-6R (potentially mediated at least in part by CRP) on schizophrenia risk. It is possible that such effects are a result of increased susceptibility to early life infection.

Hand grip strength is a widely used proxy of muscular fitness, a marker of frailty, and predictor of a range of morbidities and all-cause mortality. To investigate the genetic determinants of variation in grip strength, we perform a large-scale genetic discovery analysis in a combined sample of 195,180 individuals and identify 16 loci associated with grip strength (P

Mendelian randomization (MR) requires strong assumptions about the genetic instruments, of which the most difficult to justify relate to pleiotropy. In a two-sample MR, different methods of analysis are available if we are able to assume, M1 : no pleiotropy (fixed effects meta-analysis), M2 : that there may be pleiotropy but that the average pleiotropic effect is zero (random effects meta-analysis), and M3 : that the average pleiotropic effect is nonzero (MR-Egger). In the latter 2 cases, we also require that the size of the pleiotropy is independent of the size of the effect on the exposure. Selecting one of these models without good reason would run the risk of misrepresenting the evidence for causality. The most conservative strategy would be to use M3 in all analyses as this makes the weakest assumptions, but such an analysis gives much less precise estimates and so should be avoided whenever stronger assumptions are credible. We consider the situation of a two-sample design when we are unsure which of these 3 pleiotropy models is appropriate. The analysis is placed within a Bayesian framework and Bayesian model averaging is used. We demonstrate that even large samples of the scale used in genome-wide meta-analysis may be insufficient to distinguish the pleiotropy models based on the data alone. Our simulations show that Bayesian model averaging provides a reasonable trade-off between bias and precision. Bayesian model averaging is recommended whenever there is uncertainty about the nature of the pleiotropy.

Background: Mendelian randomization (MR) is being increasingly used to strengthen causal inference in observational studies. Availability of summary data of genetic associations for a variety of phenotypes from large genome-wide association studies (GWAS) allows straightforward application of MR using summary data methods, typically in a two-sample design. In addition to the conventional inverse variance weighting (IVW) method, recently developed summary data MR methods, such as the MR-Egger and weighted median approaches, allow a relaxation of the instrumental variable assumptions. Methods: Here, a new method - the mode-based estimate (MBE) - is proposed to obtain a single causal effect estimate from multiple genetic instruments. The MBE is consistent when the largest number of similar (identical in infinite samples) individual-instrument causal effect estimates comes from valid instruments, even if the majority of instruments are invalid. We evaluate the performance of the method in simulations designed to mimic the two-sample summary data setting, and demonstrate its use by investigating the causal effect of plasma lipid fractions and urate levels on coronary heart disease risk. Results: the MBE presented less bias and lower type-I error rates than other methods under the null in many situations. Its power to detect a causal effect was smaller compared with the IVW and weighted median methods, but was larger than that of MR-Egger regression, with sample size requirements typically smaller than those available from GWAS consortia. Conclusions: the MBE relaxes the instrumental variable assumptions, and should be used in combination with other approaches in sensitivity analyses.

Mendelian randomization investigations are becoming more powerful and simpler to perform, due to the increasing size and coverage of genome-wide association studies and the increasing availability of summarized data on genetic associations with risk factors and disease outcomes. However, when using multiple genetic variants from different gene regions in a Mendelian randomization analysis, it is highly implausible that all the genetic variants satisfy the instrumental variable assumptions. This means that a simple instrumental variable analysis alone should not be relied on to give a causal conclusion. In this article, we discuss a range of sensitivity analyses that will either support or question the validity of causal inference from a Mendelian randomization analysis with multiple genetic variants. We focus on sensitivity analyses of greatest practical relevance for ensuring robust causal inferences, and those that can be undertaken using summarized data. Aside from cases in which the justification of the instrumental variable assumptions is supported by strong biological understanding, a Mendelian randomization analysis in which no assessment of the robustness of the findings to violations of the instrumental variable assumptions has been made should be viewed as speculative and incomplete. In particular, Mendelian randomization investigations with large numbers of genetic variants without such sensitivity analyses should be treated with skepticism.

Bayesian adaptive trials have the defining feature that the probability of randomization to a particular treatment arm can change as information becomes available as to its true worth. However, there is still a general reluctance to implement such designs in many clinical settings. One area of concern is that their frequentist operating characteristics are poor or, at least, poorly understood. We investigate the bias induced in the maximum likelihood estimate of a response probability parameter, p, for binary outcome by the process of adaptive randomization. We discover that it is small in magnitude and, under mild assumptions, can only be negative - causing one's estimate to be closer to zero on average than the truth. A simple unbiased estimator for p is obtained, but it is shown to have a large mean squared error. Two approaches are therefore explored to improve its precision based on inverse probability weighting and Rao-Blackwellization. We illustrate these estimation strategies using two well-known designs from the literature.

Mendelian randomization (MR), the use of genetic variants as instrumental variables (IVs) to test causal effects, is increasingly used in aetiological epidemiology. Few of the methodological developments in MR have considered the specific situation of using genetic IVs to test the causal effect of exposures in pregnant women on postnatal offspring outcomes. In this paper, we describe specific ways in which the IV assumptions might be violated when MR is used to test such intrauterine effects. We highlight the importance of considering the extent to which there is overlap between genetic variants in offspring that influence their outcome with genetic variants used as IVs in their mothers. Where there is overlap, and particularly if it generates a strong association of maternal genetic IVs with offspring outcome via the offspring genotype, the exclusion restriction assumption of IV analyses will be violated. We recommend a set of analyses that ought to be considered when MR is used to address research questions concerned with intrauterine effects on post-natal offspring outcomes, and provide details of how these can be undertaken and interpreted. These additional analyses include the use of genetic data from offspring and fathers, examining associations using maternal non-transmitted alleles, and using simulated data in sensitivity analyses (for which we provide code). We explore the extent to which new methods that have been developed for exploring violation of the exclusion restriction assumption in the two-sample setting (MR-Egger and median based methods) might be used when exploring intrauterine effects in one-sample MR. We provide a list of recommendations that researchers should use when applying MR to test the effects of intrauterine exposures on postnatal offspring outcomes and use an illustrative example with real data to demonstrate how our recommendations can be applied and subsequent results appropriately interpreted.

The problem of selection bias has long been recognized in the analysis of two-stage trials, where promising candidates are selected in stage 1 for confirmatory analysis in stage 2. To efficiently correct for bias, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been proposed for a wide variety of trial settings, but where the population parameter estimates are assumed to be independent. We relax this assumption and derive the UMVCUE in the multivariate normal setting with an arbitrary known covariance structure. One area of application is the estimation of odds ratios (ORs) when combining a genome-wide scan with a replication study. Our framework explicitly accounts for correlated single nucleotide polymorphisms, as might occur due to linkage disequilibrium. We illustrate our approach on the measurement of the association between 11 genetic variants and the risk of Crohn's disease, as reported in Parkes and others (2007. Sequence variants in the autophagy gene IRGM and multiple other replicating loci contribute to Crohn's disease susceptibility. Nat. Gen. 39: (7), 830-832.), and show that the estimated ORs can vary substantially if both selection and correlation are taken into account.

In Phase II oncology trials, therapies are increasingly being evaluated for their effectiveness in specific populations of interest. Such targeted trials require designs that allow for stratification based on the participants' molecular characterisation. A targeted design proposed by Jones and Holmgren (JH) Jones CL, Holmgren E: 'An adaptive Simon two-stage design for phase 2 studies of targeted therapies', Contemporary Clinical Trials 28 (2007) 654-661.determines whether a drug only has activity in a disease sub-population or in the wider disease population. Their adaptive design uses results from a single interim analysis to decide whether to enrich the study population with a subgroup or not; it is based on two parallel Simon two-stage designs. We study the JH design in detail and extend it by providing a few alternative ways to control the familywise error rate, in the weak sense as well as the strong sense. We also introduce a novel optimal design by minimising the expected sample size. Our extended design contributes to the much needed framework for conducting Phase II trials in stratified medicine. © 2016 the Authors Pharmaceutical Statistics Published by John Wiley & Sons Ltd.

Background: : MR-Egger regression has recently been proposed as a method for Mendelian randomization (MR) analyses incorporating summary data estimates of causal effect from multiple individual variants, which is robust to invalid instruments. It can be used to test for directional pleiotropy and provides an estimate of the causal effect adjusted for its presence. MR-Egger regression provides a useful additional sensitivity analysis to the standard inverse variance weighted (IVW) approach that assumes all variants are valid instruments. Both methods use weights that consider the single nucleotide polymorphism (SNP)-exposure associations to be known, rather than estimated. We call this the `NO Measurement Error' (NOME) assumption. Causal effect estimates from the IVW approach exhibit weak instrument bias whenever the genetic variants utilized violate the NOME assumption, which can be reliably measured using the F-statistic. The effect of NOME violation on MR-Egger regression has yet to be studied. Methods: an adaptation of the I2 statistic from the field of meta-analysis is proposed to quantify the strength of NOME violation for MR-Egger. It lies between 0 and 1, and indicates the expected relative bias (or dilution) of the MR-Egger causal estimate in the two-sample MR context. We call it IGX2. The method of simulation extrapolation is also explored to counteract the dilution. Their joint utility is evaluated using simulated data and applied to a real MR example. Results: in simulated two-sample MR analyses we show that, when a causal effect exists, the MR-Egger estimate of causal effect is biased towards the null when NOME is violated, and the stronger the violation (as indicated by lower values of IGX2 ), the stronger the dilution. When additionally all genetic variants are valid instruments, the type I error rate of the MR-Egger test for pleiotropy is inflated and the causal effect underestimated. Simulation extrapolation is shown to substantially mitigate these adverse effects. We demonstrate our proposed approach for a two-sample summary data MR analysis to estimate the causal effect of low-density lipoprotein on heart disease risk. A high value of IGX2 close to 1 indicates that dilution does not materially affect the standard MR-Egger analyses for these data. Conclusions: : Care must be taken to assess the NOME assumption via the IGX2 statistic before implementing standard MR-Egger regression in the two-sample summary data context. If IGX2 is sufficiently low (less than 90%), inferences from the method should be interpreted with caution and adjustment methods considered.

This study focused on resolving the relationship between BMI and type 2 diabetes. The availability of multiple variants associated with BMI offers a new chance to resolve the true causal effect of BMI on type 2 diabetes; however, the properties of these associations and their validity as genetic instruments need to be considered alongside established and new methods for undertaking Mendelian randomization (MR). We explore the potential for pleiotropic genetic variants to generate bias, revise existing estimates, and illustrate value in new analysis methods. A two-sample MR approach with 96 genetic variants was used with three different analysis methods, two of which (MR-Egger and the weighted median) have been developed specifically to address problems of invalid instrumental variables. We estimate an odds ratio for type 2 diabetes per unit increase in BMI (kg/m(2)) of between 1.19 and 1.38, with the most stable estimate using all instruments and a weighted median approach (1.26 [95% CI 1.17, 1.34]). TCF7L2(rs7903146) was identified as a complex effect or pleiotropic instrument, and removal of this variant resulted in convergence of causal effect estimates from different causal analysis methods. This indicated the potential for pleiotropy to affect estimates and differences in performance of alternative analytical methods. In a real type 2 diabetes-focused example, this study demonstrates the potential impact of invalid instruments on causal effect estimates and the potential for new approaches to mitigate the bias caused.

Mendelian randomization (MR) is an increasingly important tool for appraising causality in observational epidemiology. The technique exploits the principle that genotypes are not generally susceptible to reverse causation bias and confounding, reflecting their fixed nature and Mendel’s first and second laws of inheritance. The approach is, however, subject to important limitations and assumptions that, if unaddressed or compounded by poor study design, can lead to erroneous conclusions. Nevertheless, the advent of 2-sample approaches (in which exposure and outcome are measured in separate samples) and the increasing availability of open-access data from large consortia of genome-wide association studies and population biobanks mean that the approach is likely to become routine practice in evidence synthesis and causal inference research. In this article we provide an overview of the design, analysis, and interpretation of MR studies, with a special emphasis on assumptions and limitations. We also consider different analytic strategies for strengthening causal inference. Although impossible to prove causality with any single approach, MR is a highly cost-effective strategy for prioritizing intervention targets for disease prevention and for strengthening the evidence base for public health policy.

Obesity is a highly prevalent risk factor for cardiometabolic diseases. Observational studies suggest that obesity is associated with psychiatric traits, but causal inference from such studies has several limitations. We used two-sample Mendelian randomization methods (inverse variance weighting, weighted median and MR-Egger regression) to evaluate the association of body mass index (BMI) with three psychiatric traits using data from the Genetic Investigation of Anthropometric Traits and Psychiatric Genomics consortia. Causal odds ratio estimates per 1-standard deviation increment in BMI ranged from 0.88 (95% CI: 0.62; 1.25) to 1.23 (95% CI: 0.65; 2.31) for bipolar disorder; 0.93 (0.78; 1.11) to 1.41 (0.87; 2.27) for schizophrenia; and 1.15 (95% CI: 0.92; 1.44) to 1.40 (95% CI: 1.03; 1.90) for major depressive disorder. Analyses removing potentially influential SNPs suggested that the effect estimates for depression might be underestimated. Our findings do not support the notion that higher BMI increases risk of bipolar disorder and schizophrenia. Although the point estimates for depression were consistent in all sensitivity analyses, the overall statistical evidence was weak. However, the fact that SNP-depression associations were estimated in relatively small samples reduced power to detect causal effects. This should be re-addressed when SNP-depression associations from larger studies become available.

BACKGROUND: Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative. METHODS: We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained. RESULTS: Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest. CONCLUSIONS: We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the '1-4 % split', where greater tail probability is allocated to the upper confidence bound. The 'width-optimal' interval that we present deserves further investigation.

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse-variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite-sample Type 1 error rates than the inverse-variance weighted method, and is complementary to the recently proposed MR-Egger (Mendelian randomization-Egger) regression method. In analyses of the causal effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol on coronary artery disease risk, the inverse-variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR-Egger regression methods suggest a null effect of high-density lipoprotein cholesterol that corresponds with the experimental evidence. Both median-based and MR-Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants.

In randomised controlled trials of treatments for late-stage cancer, it is common for control arm patients to receive the experimental treatment around the point of disease progression. This treatment switching can dilute the estimated treatment effect on overall survival and impact the assessment of a treatment's benefit on health economic evaluations. The rank-preserving structural failure time model of Robins and Tsiatis (Comm. Stat. 20:2609-2631) offers a potential solution to this problem and is typically implemented using the logrank test. However, in the presence of substantial switching, this test can have low power because the hazard ratio is not constant over time. Schoenfeld (Biometrika, 68:316-319) showed that when the hazard ratio is not constant, weighted versions of the logrank test become optimal. We present a weighted logrank test statistic for the late stage cancer trial context given the treatment switching pattern and working assumptions about the underlying hazard function in the population. Simulations suggest that the weighted approach can lead to large efficiency gains in either an intention-to-treat or a causal rank-preserving structural failure time model analysis compared with the unweighted approach. Furthermore, violation of the working assumptions used in the derivation of the weights only affects the efficiency of the estimates and does not induce bias or inflate the type I error rate. The weighted logrank test statistic should therefore be considered for use as part of a careful secondary, exploratory analysis of trial data affected by substantial treatment switching.

Meta-analyses are typically used to estimate the overall/mean of an outcome of interest. However, inference about between-study variability, which is typically modelled using a between-study variance parameter, is usually an additional aim. The DerSimonian and Laird method, currently widely used by default to estimate the between-study variance, has been long challenged. Our aim is to identify known methods for estimation of the between-study variance and its corresponding uncertainty, and to summarise the simulation and empirical evidence that compares them. We identified 16 estimators for the between-study variance, seven methods to calculate confidence intervals, and several comparative studies. Simulation studies suggest that for both dichotomous and continuous data the estimator proposed by Paule and Mandel and for continuous data the restricted maximum likelihood estimator are better alternatives to estimate the between-study variance. Based on the scenarios and results presented in the published studies, we recommend the Q-profile method and the alternative approach based on a 'generalised Cochran between-study variance statistic' to compute corresponding confidence intervals around the resulting estimates. Our recommendations are based on a qualitative evaluation of the existing literature and expert consensus. Evidence-based recommendations require an extensive simulation study where all methods would be compared under the same scenarios.

Seamless phase II/III clinical trials offer an efficient way to select an experimental treatment and perform confirmatory analysis within a single trial. However, combining the data from both stages in the final analysis can induce bias into the estimates of treatment effects. Methods for bias adjustment developed thus far have made restrictive assumptions about the design and selection rules followed. In order to address these shortcomings, we apply recent methodological advances to derive the uniformly minimum variance conditionally unbiased estimator for two-stage seamless phase II/III trials. Our framework allows for the precision of the treatment arm estimates to take arbitrary values, can be utilised for all treatments that are taken forward to phase III and is applicable when the decision to select or drop treatment arms is driven by a multiplicity-adjusted hypothesis testing procedure. © 2016 the Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

The funnel plot is a graphical visualization of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modeling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the center of mass of a physical system. We used this analogy to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulas and with a little help from Sherlock Holmes! Following on from the science fair, we have developed an interactive web-application (named the Meta-Analyser) to bring these ideas to a wider audience. We envisage that our application will be a useful tool for researchers when interpreting their data. First, to facilitate a simple understanding of fixed and random effects modeling approaches; second, to assess the importance of outliers; and third, to show the impact of adjusting for small study bias. This final aim is realized by introducing a novel graphical interpretation of the well-known method of Egger regression.

Moment-based estimators of the between-study variance are very popular when performing random effects meta-analyses. This type of estimation has many advantages including computational and conceptual simplicity. Furthermore, by using these estimators in large samples, valid meta-analyses can be performed without the assumption that the treatment effects follow a normal distribution. Recently proposed moment-based confidence intervals for the between-study variance are exact under the random effects model but are quite elaborate. Here, we present a much simpler method for calculating approximate confidence intervals of this type. This method uses variance-stabilising transformations as its basis and can be used for a very wide variety of moment-based estimators in both the random effects meta-analysis and meta-regression models.

When developing a new diagnostic test for a disease, there are often multiple candidate classifiers to choose from, and it is unclear if any will offer an improvement in performance compared with current technology. A two-stage design can be used to select a promising classifier (if one exists) in stage one for definitive validation in stage two. However, estimating the true properties of the chosen classifier is complicated by the first stage selection rules. In particular, the usual maximum likelihood estimator (MLE) that combines data from both stages will be biased high. Consequently, confidence intervals and p-values flowing from the MLE will also be incorrect. Building on the results of Pepe et al. (SIM 28:762-779), we derive the most efficient conditionally unbiased estimator and exact confidence intervals for a classifier's sensitivity in a two-stage design with arbitrary selection rules; the condition being that the trial proceeds to the validation stage. We apply our estimation strategy to data from a recent family history screening tool validation study by Walter et al. (BJGP 63:393-400) and are able to identify and successfully adjust for bias in the tool's estimated sensitivity to detect those at higher risk of breast cancer.

BACKGROUND: the number of Mendelian randomization analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. However, some genetic variants may not be valid instrumental variables, in particular due to them having more than one proximal phenotypic correlate (pleiotropy). METHODS: We view Mendelian randomization with multiple instruments as a meta-analysis, and show that bias caused by pleiotropy can be regarded as analogous to small study bias. Causal estimates using each instrument can be displayed visually by a funnel plot to assess potential asymmetry. Egger regression, a tool to detect small study bias in meta-analysis, can be adapted to test for bias from pleiotropy, and the slope coefficient from Egger regression provides an estimate of the causal effect. Under the assumption that the association of each genetic variant with the exposure is independent of the pleiotropic effect of the variant (not via the exposure), Egger's test gives a valid test of the null causal hypothesis and a consistent causal effect estimate even when all the genetic variants are invalid instrumental variables. RESULTS: We illustrate the use of this approach by re-analysing two published Mendelian randomization studies of the causal effect of height on lung function, and the causal effect of blood pressure on coronary artery disease risk. The conservative nature of this approach is illustrated with these examples. CONCLUSIONS: an adaption of Egger regression (which we call MR-Egger) can detect some violations of the standard instrumental variable assumptions, and provide an effect estimate which is not subject to these violations. The approach provides a sensitivity analysis for the robustness of the findings from a Mendelian randomization investigation.

Multi-armed bandit problems (MABPs) are a special type of optimal control problem well suited to model resource allocation under uncertainty in a wide variety of contexts. Since the first publication of the optimal solution of the classic MABP by a dynamic index rule, the bandit literature quickly diversified and emerged as an active research topic. Across this literature, the use of bandit models to optimally design clinical trials became a typical motivating application, yet little of the resulting theory has ever been used in the actual design and analysis of clinical trials. To this end, we review two MABP decision-theoretic approaches to the optimal allocation of treatments in a clinical trial: the infinite-horizon Bayesian Bernoulli MABP and the finite-horizon variant. These models possess distinct theoretical properties and lead to separate allocation rules in a clinical trial design context. We evaluate their performance compared to other allocation rules, including fixed randomization. Our results indicate that bandit approaches offer significant advantages, in terms of assigning more patients to better treatments, and severe limitations, in terms of their resulting statistical power. We propose a novel bandit-based patient allocation rule that overcomes the issue of low power, thus removing a potential barrier for their use in practice.

The Gittins index provides a well established, computationally attractive, optimal solution to a class of resource allocation problems known collectively as the multi-arm bandit problem. Its development was originally motivated by the problem of optimal patient allocation in multi-arm clinical trials. However, it has never been used in practice, possibly for the following reasons: (1) it is fully sequential, i.e. the endpoint must be observable soon after treating a patient, reducing the medical settings to which it is applicable; (2) it is completely deterministic and thus removes randomization from the trial, which would naturally protect against various sources of bias. We propose a novel implementation of the Gittins index rule that overcomes these difficulties, trading off a small deviation from optimality for a fully randomized, adaptive group allocation procedure which offers substantial improvements in terms of patient benefit, especially relevant for small populations. We report the operating characteristics of our approach compared to existing methods of adaptive randomization using a recently published trial as motivation.

In this paper, we review the adaptive design methodology of Li et al. (Biostatistics 3:277-287) for two-stage trials with mid-trial sample size adjustment. We argue that it is closer in principle to a group sequential design, in spite of its obvious adaptive element. Several extensions are proposed that aim to make it even more attractive and transparent alternative to a standard (fixed sample size) trial for funding bodies to consider. These enable a cap to be put on the maximum sample size and for the trial data to be analysed using standard methods at its conclusion. The regulatory view of trials incorporating unblinded sample size re-estimation is also discussed.

The two-stage drop-the-loser design provides a framework for selecting the most promising of K experimental treatments in stage one, in order to test it against a control in a confirmatory analysis at stage two. The multistage drop-the-losers design is both a natural extension of the original two-stage design, and a special case of the more general framework of Stallard & Friede () (Stat. Med. 27, 6209-6227). It may be a useful strategy if deselecting all but the best performing treatment after one interim analysis is thought to pose an unacceptable risk of dropping the truly best treatment. However, estimation has yet to be considered for this design. Building on the work of Cohen & Sackrowitz () (Stat. Prob. Lett. 8, 273-278), we derive unbiased and near-unbiased estimates in the multistage setting. Complications caused by the multistage selection process are shown to hinder a simple identification of the multistage uniform minimum variance conditionally unbiased estimate (UMVCUE); two separate but related estimators are therefore proposed, each containing some of the UMVCUEs theoretical characteristics. For a specific example of a three-stage drop-the-losers trial, we compare their performance against several alternative estimators in terms of bias, mean squared error, confidence interval width and coverage.

Point estimation for the selected treatment in a two-stage drop-the-loser trial is not straightforward because a substantial bias can be induced in the standard maximum likelihood estimate (MLE) through the first stage selection process. Research has generally focused on alternative estimation strategies that apply a bias correction to the MLE; however, such estimators can have a large mean squared error. Carreras and Brannath (Stat. Med. 32:1677-90) have recently proposed using a special form of shrinkage estimation in this context. Given certain assumptions, their estimator is shown to dominate the MLE in terms of mean squared error loss, which provides a very powerful argument for its use in practice. In this paper, we suggest the use of a more general form of shrinkage estimation in drop-the-loser trials that has parallels with model fitting in the area of meta-analysis. Several estimators are identified and are shown to perform favourably to Carreras and Brannath's original estimator and the MLE. However, they necessitate either explicit estimation of an additional parameter measuring the heterogeneity between treatment effects or a quite unnatural prior distribution for the treatment effects that can only be specified after the first stage data has been observed. Shrinkage methods are a powerful tool for accurately quantifying treatment effects in multi-arm clinical trials, and further research is needed to understand how to maximise their utility.

The process of undertaking a meta-analysis involves a sequence of decisions, one of which is deciding which measure of treatment effect to use. In particular, for comparative binary data from randomised controlled trials, a wide variety of measures are available such as the odds ratio and the risk difference. It is often of interest to know whether important conclusions would have been substantively different if an alternative measure had been used. Here we develop a new type of sensitivity analysis that incorporates standard measures of treatment effect. Thus, rather than examining the implications of a variety of measures in an ad hoc manner, we can simultaneously examine an entire family of possibilities, including the odds ratio, the arcsine difference and the risk difference.

BACKGROUND: in 2011, Royston et al. described technical details of a two-arm, multi-stage (TAMS) design. The design enables a trial to be stopped part-way through recruitment if the accumulating data suggests a lack of benefit of the experimental arm. Such interim decisions can be made using data on an available 'intermediate' outcome. At the conclusion of the trial, the definitive outcome is analyzed. Typical intermediate and definitive outcomes in cancer might be progression-free and overall survival, respectively. In TAMS designs, the stopping rule applied at the interim stage(s) affects the sampling distribution of the treatment effect estimator, potentially inducing bias that needs addressing. METHODS: We quantified the bias in the treatment effect estimator in TAMS trials according to the size of the treatment effect and for different designs. We also retrospectively 'redesigned' completed cancer trials as TAMS trials and used the bootstrap to quantify bias. RESULTS: in trials in which the experimental treatment is better than the control and which continue to their planned end, the bias in the estimate of treatment effect is small and of no practical importance. In trials stopped for lack of benefit at an interim stage, the treatment effect estimate is biased at the time of interim assessment. This bias is markedly reduced by further patient follow-up and reanalysis at the planned 'end' of the trial. CONCLUSIONS: Provided that all patients in a TAMS trial are followed up to the planned end of the trial, the bias in the estimated treatment effect is of no practical importance. Bias correction is then unnecessary.

Two-stage trial designs provide the flexibility to stop early for efficacy or futility and are popular because they have a smaller sample size on average than a traditional trial has with the same type I and II error rates. This makes them financially attractive but also has the ethical benefit of reducing, in the long run, the number of patients who are given ineffective treatments. Designs that minimise the expected sample size are often referred to as 'optimal'. However, two-stage designs can impart a substantial bias into the parameter estimate at the end of the trial. In this paper, we argue that the expected performance of one's chosen estimation method should also be considered when deciding on a two-stage trial design. We review the properties of standard and bias-adjusted maximum likelihood estimators as well as mean and median unbiased estimators. We then identify optimal two-stage design and analysis procedures that balance projected sample size considerations with those of estimator performance. We make available software to implement this new methodology.

Meta-analyses of individual patient data (IPD) provide a strong and authoritative basis for evidence synthesis. IPD are particularly useful when the outcome of interest is the time to an event. Methodological developments now enable the meta-analysis of time-to-event IPD using a single model, allowing treatment effect and across-trial heterogeneity parameters to be estimated simultaneously. This differs from the standard approaches used with aggregate data, and also predominantly with IPD. Facilitated by a simulation study, we investigate what these new 'one-stage' random-effects models offer over standard 'two-stage' approaches. We find that two-stage approaches represent a robust, reliable and easily implementable way to estimate treatment effects and account for heterogeneity. Nevertheless, one-stage models can be used to provide a deeper insight into the data. Software for fitting one-stage Cox models with random effects using Restricted Maximum Likelihood methodology is made available, and its use demonstrated on an IPD meta-analysis assessing post-operative radio therapy for patients with non-small cell lung cancer. Copyright © 2011 John Wiley & Sons, Ltd.

'Instrumental Variable' (IV) methods provide a basis for estimating an exposure's causal effect on the risk of disease. In Mendelian randomization studies, where genetic information plays the role of the IV, IV analyses are routinely performed on case-control data, rather than prospectively collected observational data. Although it is a well-appreciated fact that ascertainment bias may invalidate such analyses, ad hoc assumptions and approximations are made to justify their use. In this paper we attempt to explain and clarify why they may fail and show how they can be adjusted for improved performance. In particular, we propose consistent estimators of the causal relative risk and odds ratio if a priori knowledge is available regarding either the population disease prevalence or the population distribution of the IV (e.g. population allele frequencies). We further show that if no such information is available, approximate estimators can be obtained under a rare disease assumption. We illustrate this with matched case-control data from the recently completed EPIC study, from which we attempt to assess the evidence for a causal relationship between C-reactive protein levels and the risk of Coronary Artery Disease.

BACKGROUND: Clinical researchers have often preferred to use a fixed effects model for the primary interpretation of a meta-analysis. Heterogeneity is usually assessed via the well known Q and I2 statistics, along with the random effects estimate they imply. In recent years, alternative methods for quantifying heterogeneity have been proposed, that are based on a 'generalised' Q statistic. METHODS: We review 18 IPD meta-analyses of RCTs into treatments for cancer, in order to quantify the amount of heterogeneity present and also to discuss practical methods for explaining heterogeneity. RESULTS: Differing results were obtained when the standard Q and I2 statistics were used to test for the presence of heterogeneity. The two meta-analyses with the largest amount of heterogeneity were investigated further, and on inspection the straightforward application of a random effects model was not deemed appropriate. Compared to the standard Q statistic, the generalised Q statistic provided a more accurate platform for estimating the amount of heterogeneity in the 18 meta-analyses. CONCLUSIONS: Explaining heterogeneity via the pre-specification of trial subgroups, graphical diagnostic tools and sensitivity analyses produced a more desirable outcome than an automatic application of the random effects model. Generalised Q statistic methods for quantifying and adjusting for heterogeneity should be incorporated as standard into statistical software. Software is provided to help achieve this aim.

Genetic markers can be used as instrumental variables, in an analogous way to randomization in a clinical trial, to estimate the causal relationship between a phenotype and an outcome variable. Our purpose is to extend the existing methods for such Mendelian randomization studies to the context of multiple genetic markers measured in multiple studies, based on the analysis of individual participant data. First, for a single genetic marker in one study, we show that the usual ratio of coefficients approach can be reformulated as a regression with heterogeneous error in the explanatory variable. This can be implemented using a Bayesian approach, which is next extended to include multiple genetic markers. We then propose a hierarchical model for undertaking a meta-analysis of multiple studies, in which it is not necessary that the same genetic markers are measured in each study. This provides an overall estimate of the causal relationship between the phenotype and the outcome, and an assessment of its heterogeneity across studies. As an example, we estimate the causal relationship of blood concentrations of C-reactive protein on fibrinogen levels using data from 11 studies. These methods provide a flexible framework for efficient estimation of causal relationships derived from multiple studies. Issues discussed include weak instrument bias, analysis of binary outcome data such as disease risk, missing genetic data, and the use of haplotypes.

Asymmetry in the funnel plot for a meta-analysis suggests the presence of dissemination bias. This may be caused by publication bias through the decisions of journal editors, by selective reporting of research results by authors or by a combination of both. Typically, study results that are statistically significant or have larger estimated effect sizes are more likely to appear in the published literature, hence giving a biased picture of the evidence-base. Previous statistical approaches for addressing dissemination bias have assumed only a single selection mechanism. Here we consider a more realistic scenario in which multiple dissemination processes, involving both the publishing authors and journals, are operating. In practical applications, the methods can be used to provide sensitivity analyses for the potential effects of multiple dissemination biases operating in meta-analysis.

The quantile approximation method has recently been proposed as a simple method for deriving confidence intervals for the treatment effect in a random effects meta-analysis. Although easily implemented, the quantiles used to construct intervals are derived from a single simulation study. Here it is shown that altering the study parameters, and in particular introducing changes to the distribution of the within-study variances, can have a dramatic impact on the resulting quantiles. This is further illustrated analytically by examining the scenario where all trials are assumed to be the same size. A more cautious approach is therefore suggested, where the conventional standard normal quantile is used in the primary analysis, but where the use of alternative quantiles is also considered in a sensitivity analysis.

Odds ratios or other effect sizes estimated from genome scans are upwardly biased, because only the top-ranking associations are reported, and moreover only if they reach a defined level of significance. No unbiased estimate exists based on data selected in this fashion, but replication studies are routinely performed that allow unbiased estimation of the effect sizes. Estimation based on replication data alone is inefficient in the sense that the initial scan could, in principle, contribute information on the effect size. We propose an unbiased estimator combining information from both the initial scan and the replication study, which is more efficient than that based just on the replication. Specifically, we adjust the standard combined estimate to allow for selection by rank and significance in the initial scan. Our approach explicitly allows for multiple associations arising from a scan, and is robust to mis-specification of a significance threshold. We require replication data to be available but argue that, in most applications, estimates of effect sizes are only useful when associations have been replicated. We illustrate our approach on some recently completed scans and explore its efficiency by simulation.

Correction for ascertainment bias is a vital part of the analysis of genetic epidemiology studies that needs to be undertaken whenever subjects are not recruited at random. Adjustment often requires extensive numerical integration, which can be very slow or even computationally infeasible, especially if the model includes many fixed and random effects. In this paper we propose a two-stage method for ascertainment bias correction. In the first stage we estimate parameters that pertain to the ascertained population, that is the population that would be selected into the sample if the ascertainment criterion were applied to everyone. In the second stage we convert the estimates for the ascertained population into general population parameter estimates. We illustrate the method with simulations based on a simple model and then describe how the method can be used with complex models. The two-stage approach avoids some of the integration required in direct adjustment, hence speeding up the process of model fitting.